Orientation analysis of fibers is widely applied in the fields of medical, material and life sciences. The orientation information allows predicting properties and behavior of materials to validate and guide a fabrication process of materials with controlled fiber orientation. Meanwhile, development of detector systems for high-resolution non-invasive 3D imaging techniques led to a significant increase in the amount of generated data per a sample up to dozens of gigabytes. Though plenty of 3D orientation estimation algorithms were developed in recent years, neither of them can process large datasets in a reasonable amount of time. This fact complicates the further analysis and makes impossible fast feedback to adjust fabrication parameters. In this work, we present a new method for quantifying the 3D orientation of fibers. The GPU implementation of the proposed method surpasses another popular method for 3D orientation analysis regarding accuracy and speed. The validation of both methods was performed on a synthetic dataset with varying parameters of fibers. Moreover, the proposed method was applied to perform orientation analysis of scaffolds with different fibrous micro-architecture studied with the synchrotron μCT imaging setup. Each acquired dataset of size 600x600x450 voxels was analyzed in less 2 minutes using standard PC equipped with a single GPU.